Question

4x2 + 4bx - (a - b) = 0 ​

Answer 1

$\mathtt{4x²+4bx-(a²-b²) = 0}$

$\implies\mathtt{4x²+4bx = (a²-b²)}$

$\texttt{adding } \mathtt{b²} \texttt{ to both sides}$

$\implies\mathtt{4x²+4bx+b² = a²-b²+b²}$

$\implies\mathtt{(2x+b)² = a²}$

$\implies\mathtt{(2x+b) = ± \sqrt{a²}}$

$\implies\mathtt{(2x+b) = ±a}$

$\implies\mathtt{2x+b = a}\;\;\;\;\texttt{or}\;\;\;\;\mathtt{2x+b = -a}$

$\implies\mathtt{2x = a-b}\;\;\;\;\texttt{or}\;\;\;\;\mathtt{2x+b = -a-b}$

$\implies\mathtt{x = \Large\frac{a-b}{2}}\normalsize\;\;\;\;\texttt{or}\;\;\;\;\mathtt{x = \Large\frac{-a-b}{2}}$